Optical resonators are electro-optical devices that are included in optical feedback loops to store energy having only specific resonant mode frequencies. Optical resonators are often small in size, having diameters on the order of millimeters, and may be used in many electro-optical system applications, including optical sensors for biological and chemical compounds, electro-optical oscillators and modulators, and tunable optical filters. The optical resonators are curved optical waveguides, for example, a cylinder, a sphere, or a toroid within which light is internally reflected at the inner surface of the optical resonator.
Optical resonators can support resonator modes of light called whispering-gallery modes (“WGMs”), and thus, are often referred to as whispering-gallery mode resonators. WGMs occur when light having an evanescent wave component travels via internal reflection around the periphery of the optical resonator. The evanescent waves extend beyond the optical resonator's outer surface and may be coupled into an adjacent optical coupler as long as the optical coupler is located within the extent of the evanescent wave, typically on the order of the light's wavelength.
Many optical resonators which propagate WGMs of light have extremely low transmission loses, and as a result, have a very high quality factor (“Q”). High-Q optical resonators are desirable because the higher the Q, the longer the amount of time the internally reflected light remains within the optical resonator and the greater the reduction of the spectral line width and phase noise. The ultimate intrinsic Q of the optical resonator (Q0) is limited by the optical losses of the resonator material. Optical resonators having radiuses of 10 to a few hundred micrometers have been produced with Q's in excess of 1×109 (see V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett. A37, 393 (1989); L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, S. Haroche, Europhys. Lett. 23, 327 (1993)). In particular, a Q in excess of 1×1010 was demonstrated for optical resonators, and a Q of 1011 is expected for glass microsphere optical resonators with a resonant wavelength of light at 1550 nanometers, where the intrinsic loss of glass is a minimum.
Coupling to WGMs of the optical resonator can be accomplished through an evanescent wave from an adjacent optical coupler. Coupling losses between the optical coupler and the optical resonator are exponentially dependent upon the distance d between the surface of the optical coupler and the optical resonator ˜ exp (−d/r*), where r* is the effective scale length of evanescent field of the resonator for the excited WGM as expressed in the following equation:r*=λ√{square root over ((4n(nres/nout)2−1))}
where:                λ is the wavelength of light evanescently coupled between the optical coupler and the optical resonator;        nres is the index of refraction of the optical resonator; and        nout is the index of refraction outside the surface of the optical resonator.        
Because the optical resonator and optical coupler are small in size they may be integrated within small housings or devices that can be incorporated into various optical or electro-optical systems including opto-electronic oscillators (“OEOs”) which may be used to generate microwave frequency signals. In addition to having an optical resonator. OEOs include an electrically-controlled optical modulator included in a feedback loop having a gain greater than one. The opto-electronic feedback loops includes a photodetector for conversion of optical signals into electrical signals that are used to control the modulator and sustain the optical signal.
In general, many modes of oscillation may oscillate simultaneously in an OEO. The optical resonator and the electro-optic feedback loop each generate their own resonant modes. Mode matching between the modes of the optical resonator and the modes of the electro-optic feedback loop is required. A mode that does not satisfy the mode matching conditions is subject to loss. Because of the mode matching requirements, the mode spacing of the electro-optic feedback loop is limited to the narrow mode spacing of the high-Q optical resonator.
One challenge associated with mass producing integrated electro-optical systems that include optical resonators and electro-optic feedback loops is providing for ease and repeatability in accurately setting and maintaining the exact position of the components that make up the electro-optical system.
Another challenge associated with mass producing these integrated electro-optical systems is related to the waveguide that is used for evanescent coupling of light between the optical resonator and the electro-optic feedback loop. The basis for optical coupling using a waveguide is in-phase matching of the field of the waveguide to the field in the optical resonator's WGM which is accomplished by cutting the waveguide 10, for example an optical fiber 12, at the angle Φ as shown in FIG. 1. In order to satisfy the phase matching requirement Φ=arcsin(nres/nwg), where nres is the effective index of refraction for azimuthal propagation of the WGMs as closed waves circulating in a microsphere optical resonator 14, and nwg is the effective index of refraction for the light guided by the waveguide. The precision cut of the waveguide to create the required angle is difficult to implement. This is especially true in the case of semiconductor waveguides where efficient growth and the cleave angle relate to the orientation of the waveguide material. In addition, the above mentioned angle phase matching scheme is not suitable for cases in which the indices of refraction of the waveguide and the optical resonator are significantly different, for example, when the waveguide is a silicon optical fiber having a core index of refraction of 1.46 and the optical resonator is made of lithium niobate having an index of refraction of 2.06.
Therefore, there is a need for electro-optical systems having a reduced number of components that must be aligned during the fabrication process. Furthermore, there is a need for electro-optical systems in which the components are configured such that the precise angle cut of the waveguide is not required.